Question

How do you solve `x^2 + 9x + 8 = 0` by factoring?

Answer 1

The solutions are
`color(blue)( x=-1`
`color(blue)(x=-8`

Explanation:

`x^2+9x+8=0`

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like `ax^2 + bx+ c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c =1*8 =8`
and
`N_1 +N_2 = b = 9`

After trying out a few numbers we get `N_1 = 8` and `N_2=1`

`8*1 = 8`, and `8+ 1= 9`

`x^2+9x+8=x^2+8x+1x+8`

`x(x+8) +1(x+8)=0`

`color(blue)((x+1)(x+8))=0` is the factorised form of the equation.

Now we equate the factors to the R.H.S(0)
`x+1=0,color(blue)( x=-1`
`x+8=0, color(blue)(x=-8`